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Lorentz transformations (time dilation)

  1. Sep 4, 2014 #1
    1. The problem statement, all variables and given/known data

    A rocket ship carrying passengers blasts off to go from
    New York to Los Angeles, a distance of about 5000 km.
    (a) How fast must the rocket ship go to have its own
    length shortened by 1%? (b) Ignore effects of general
    relativity and determine how much time the rocket
    ship’s clock and the ground-based clocks differ when
    the rocket ship arrives in Los Angeles.

    2. Relevant equations

    Since I solved for (a) and got the correct answer (0.14c or approx. 4.2x107m/s), here is the equation for (b) that I used:

    T' = To/(sqrt(1-β2)

    alternate formula:

    t'2 - t'1 = ((t2 - t1) - (v/c^2)(x2 - x1)/(sqrt(1-β^2)

    3. The attempt at a solution

    Total travel time = 0.119s (5E6/4.2E7)
    Velocity = 4.2E7

    So:

    T' = 0.119/(sqrt(1-4.2E7^2/3E8^2))
    This gave me 1.2E-1s (or about 120ms)

    alternately (second formula):

    T' = (0.119 - (4.2E7/c^2)(5E6)/(sqrt(1-(4.2E7^2/c^2)))
    This gave me 1.17E-1s (or about 120ms)

    ---------------------------
    It seems like both are giving me the same answer, but are off by a factor of 100 (since both round to 120ms and the correct answer is 1.2ms). Can someone please let me know where I'm going wrong?
     
  2. jcsd
  3. Sep 4, 2014 #2

    vela

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    You've calculated the time elapsed on the two clocks, but the question is asking for the difference between the two clocks.
     
  4. Sep 4, 2014 #3
    Oh wow, I can't believe I overlooked that fact. Thank you.
     
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